Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
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Abstract (arXiv)
Out-of-equilibrium quantum many-body systems exhibit rapid correlation buildup that underlies many emerging phenomena. Exact wave-function methods to describe this scale exponentially with particle number; simpler mean-field approaches neglect essential two-particle correlations. The time-dependent two-particle reduced density matrix (TD2RDM) formalism offers a middle ground by propagating the two-particle reduced density matrix (2RDM) and closing the BBGKY hierarchy with a reconstruction of the three-particle cumulant. But the validity and existence of time-local reconstruction functionals ignoring memory effects remain unclear across different dynamical regimes. We show that a neural ODE model trained on exact 2RDM data (no dimensionality reduction) can reproduce its dynamics without any explicit three-particle information -- but only in parameter regions where the Pearson correlation between the two- and three-particle cumulants is large. In the anti-correlated or uncorrelated regime, the neural ODE fails, indicating that no simple time-local functional of the instantaneous two-particle cumulant can capture the evolution. The magnitude of the time-averaged three-particle-correlation buildup appears to be the primary predictor of success: For a moderate correlation buildup, both neural ODE predictions and existing TD2RDM reconstructions are accurate, whereas stronger values lead to systematic breakdowns. These findings pinpoint the need for memory-dependent kernels in the three-particle cumulant reconstruction for the latter regime. Our results place the neural ODE as a model-agnostic diagnostic tool that maps the regime of applicability of cumulant expansion methods and guides the development of non-local closure schemes. More broadly, the ability to learn high-dimensional RDM dynamics from limited data opens a pathway to fast, data-driven simulation of correlated quantum matter.
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References · 18
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- 2020Does the Markov Decision Process Fit the Data: Testing for the Markov Property in Sequential Decision Makingcited by 30
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- 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
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- 2023Testing for the Markov Property in Time Series via Deep Conditional Generative Learningcited by 9
- 2024Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equationscited by 7
- 2022Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structurescited by 5
- 2021Scaling of neural-network quantum states for time evolutioncited by 4
- 2025Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamicscited by 3
- 2025Efficient Manifold-Constrained Neural ODE for High-Dimensional Datasetscited by 2
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